Exercise 99 Page 427

Practice makes perfect

A number written in scientific notation usually expresses a very large or very small number by writing its value as the product of the number's first nonzero digit and 10 to some power. Let's look at some examples.

Standard Notation	Scientific Notation
5 0 000 000 000	5 * 10^(10)
5 00 000	5 * 10^5
5 0	5 * 10^1
5	5 * 10^0
0.5	5 * 10^(- 1)
0.00005	5 * 10^(- 5)
0.0000000005	5 * 10^(- 10)

To change from standard form to scientific notation, we need to move the decimal until the resulting number is greater than 1 and less than 10. The number of places the decimal moves is the exponent of 10. Let's take a look at the given number. 4 9.63 In this case, the number is greater than 10, so the decimal point will move to the left. We only need to move the decimal one place, so this is the power of 10.

This means that the scientific notation of 49.63 is 4.963 * 10^1. Standard Form:& 49.63 Scientific Notation:& 4.963 * 10^1

Let's consider the given number.

0.0000005 In this case, the number is less than 10, so the decimal point will move to the right. There are seven places before the first nonzero digit, so this is the power of 10.

This means that the scientific notation of 0.0000005 is 5 * 10^(- 7). Standard Form:& 0.0000005 Scientific Notation:& 5* 10^(- 7)

We are given the following number.

3 120 000 000 The number is greater than 10, meaning that the decimal point will move to the left. There are nine places after the first digit, so this is the power of 10.